Final answer:
To convert the angle 13° 38′ 35″ to decimal degrees, we divide the minutes (38) by 60 and the seconds (35) by 3600, then add these to the degree part (13), which gives us 13.643°. Rounding to the nearest hundredth gives 13.64°.
Step-by-step explanation:
The student's question involves converting an angle from degrees, minutes and seconds to decimal degrees. To do this, we must understand that 1 degree is equal to 60 minutes, and 1 minute is equal to 60 seconds. Therefore, we need to convert the minutes and seconds portion of the angle into a decimal value in degrees.
Firstly, we convert the minutes to degrees by dividing by 60 (since there are 60 minutes in a degree):
38′ ÷ 60 = 0.6333° (repeating).
Next, we convert the seconds to degrees by dividing by 3600 (since there are 3600 seconds in a degree):
35″ ÷ 3600 = 0.0097° (repeating).
We then add these decimal values to the whole degrees part of the angle:
13° + 0.6333° + 0.0097° = 13.643°.
Finally, we round this sum to the nearest hundredth as per the question, which gives us: 13.64°.
The answer choice that correctly represents this calculation is d) 13.64°.